Game-System Idea

Elements:
-Wind/Lightning
-Water/Ice
-Fire/Heat
-Earth/Metal
-Darkness/Space
-Light/Spirit

Status:
Strength (Earth)
Intelligence (Water)
Endurance (Fire)
Agility (Wind)
Cunning (Darkness)
Charity (Light)

The game system works similar to a date sim game, but there is a few key differences. For starters, there is a difficulty setting: Fantasy, Mortal, Cardinal, and Harbinger. Fantasy lets you do what you want, the game basically playing itself. The only thing about Fantasy mode is that the True Route is locked (After all, if our protagonist doesn't put in the effort, he can't expect to change things.) Mortal mode is the game's Easy mode, with a very generous amount of time offered to increase your stats (90 in-game days), and "fights" giving you plenty of hints on how to proceed. Cardinal mode is the Normal difficulty, with less time to grind (80 days) and hints only appearing for certain fights. Harbinger mode is the Hard mode, and you basically have to already know how to minmax in order to survive with the short time (70 days) and be prepared to quick save and quick load a lot because the fights have no hints.
Second, there is semi-random events that occur during your stat leveling. On Mortal mode, you only get bonus effects that amplify your stat gains. On Cardinal, there's an even mix of bonuses and negative events that prevent you from increasing a stat for a set time. Harbinger mode is nothing but negative events. Though, to be fair, you roll them all at the start of a week and each event has a set start and end date, and none of the negatives will last longer than 3 days.
Thirdly, the first four stats can only be raised in the morning, while the last two can be only raised in the afternoon or night events (Unless you roll a perk on Mortal and Cardinal). But, Monday though Friday, the morning event allows you to grind 2 stats (To go with the fact that the MC is a teacher who teaches an AM and a PM class.) While on Saturdays and Sundays, you can gain a major boost on one stat.
Fourth, to prevent people from just grinding all the way through like they do in other stat-raisers, your afternoon and night events are also where you increase your social standing among the story's characters as well as the love interest of your choice. So failure to keep up your social circle will result in total failure. As an added "bonus" you have some events that you MUST attent if you want to secure a particular route or ending (These events are clearly marked on Mortal, a hint is given on Cardinal, and no warning is given on Harbinger).
Lastly, and this is where that mention of fights comes from, is that you do have in-game battles. Once the battles commence, you have a set amount of time to grind your stats until you are challenged. During this time you can choose to spend time watching your oppnent at night, giving you hints on how to counter their attacks (Giving you a look at their move list and generating hints). You can also learn new skills by befriending the characters and strengthening your ties with your romantic interest (So even more reason to not neglect the social events!).
The battles are also why I listed elements next to a stat: Each time you raise a specific stat, your resistance to that element is increased while also allowing you to use stronger attacks in the elemental tier. Be at or above the recommended level for each stat and you can shrug off more mistakes while dealing decent damage. Be under-leveled and you'll not only be killed easily, you also deal less damage overall.
As for how the battles are handled? Well, there's a button that will appear on-screen. When you select it, a list of abilities you can use will appear. Use the proper ability at the right time and you'll advance the fight. Use an incorrect one or time it wrong and you'll take damage, making you try to attack again. This is where watching your opponent comes in handy, since certain keywords will be highlighted (On anything less than Harbinger, and only if you watched enough of your opponent's fights on Cardinal to gain the hints) allowing you to react better.

Lastly, there's one more interesting thing to note of this system: the choice to finish your opponent. Finish them and you'll gain their strongest ability as well as a permanent stat boost but lose the character's social bonuses (Said bonuses TBD). Spare them and you will immediately max their feelings towards you, giving you their social bonuses and allowing you to have them boost a certain stat for a short time (The boosted stat depends on their particular skillset, but useful nonetheless since you might roll a bad event that keeps you from reaching the minimum on a certain stat).

Much of this system might be tweaked, but this is more or less what I've come up with.